Thanks for posting your query at DoctorSpring.com. I can understand your concern.
The rough and discolored patch seems to be due to an allergy which we refer to as eczema.
I would recommend application of cortisone cream mixed with neosporin cream over the affected area.
It will resolve the patch. Also make sure to apply a moisturizing cream.
Hope this helps, Please feel free to ask any follow-up queries.